The profit made on an item sold for ₹2200 is equal to the loss incurred when it is sold for ₹1800. What will be the profit or los…

Question

The profit made on an item sold for ₹2200 is equal to the loss incurred when it is sold for ₹1800. What will be the profit or loss percentage if the item is sold for ₹2050?

1. A. Profit of 2.25%
2. B. Loss of 3.5%
3. C. Profit of 2.5% (Correct answer)
4. D. Loss of 4.25%

Correct Answer

Option C — Profit of 2.5%

Detailed Solution & Explanation

The correct answer is Profit of 2.5%.

Key Points

• If the profit at one price equals the loss at another, the cost price is exactly the average of the two prices:
  • CP = (2200 + 1800) / 2 = ₹2,000
• Verify: selling at 2,200 gives a ₹200 profit, and selling at 1,800 gives a ₹200 loss — equal, as stated.
• At ₹2,050 the profit is 2,050 − 2,000 = ₹50.
• Profit % = (50 / 2000) × 100 = 2.5%.
• The midpoint shortcut avoids setting up simultaneous equations and is worth memorising: CP = (SP₁ + SP₂)/2 whenever profit and loss are equal in rupees.

Additional Information

• The midpoint result generalises: whenever profit at SP₁ equals loss at SP₂, the cost price is (SP₁ + SP₂)/2.
• Core relations: Profit = SP − CP, Profit % = (Profit / CP) × 100, and profit percentage is always computed on the cost price unless stated otherwise.
• The related identity for equal percentage profit and loss on two equal selling prices is a net loss of x²/100 percent — a different situation with a different formula, and a common confusion.

प्रश्न (हिन्दी में)

₹2200 में बेची गई वस्तु पर हुआ लाभ ₹1800 में बेचने पर हुई हानि के बराबर है। यदि वस्तु ₹2050 में बेची जाए तो लाभ या हानि प्रतिशत क्या होगा?

1. A. 2.25% का लाभ
2. B. 3.5% की हानि
3. C. 2.5% का लाभ
4. D. 4.25% की हानि